Harmonic Analysis And Fractal Analysis Over Local Fields And Applications

This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.

The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Contents:PreliminaryCharacter Group Γp of Local Field KpHarmonic Analysis on Local FieldsFunction Spaces on Local FieldsFractal Analysis on Local FieldsFractal PDE on Local FieldsApplications to Medicine Science
Readership: Undergraduate students, graduate students and researchers.Keywords:Harmonic Analysis;Fractal Analysis;Fractal Geometry;Local Field;p-adic FieldReview:Key Features:It is the first after Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research area; although there were many papers about local fields since 1970's, but there is no systematic writings for this subjectIt contains the construction of "calculus on local fields" based on pseudo-differential operator and the applications of this new type of calculus, whereas this object is not touched in other similar writingsIt illustrates "fractal analysis on local fields", whereas most papers and writings about fractals are based on Euclidean space. Readers may find the advantages of fractal analysis on local fields